Most amateur brewers fail to realize that yeast is the most important ingredient in brewing. Pitching a large healthy culture is necessary to prevent household bacteria from overwhelming one's pitching yeast during the growth phase. Brewers sanitize their equipment. Sanitizing is not the same thing as sterilizing. Santizing equipment merely reduces the amount of microflora present on one's fermenting gear down to level where one's pitching yeast has a chance of overwhelming it during the growth phase.
Ninety-nine percent of all beer infections are the result of poor yeast handling. Fermentation is little more than controlled spoilage. Bacteria cells divide every thirty minutes. Yeast cells divide every nineties minutes; therefore, one needs to pitch enough clean yeast to out compete any other microflora that may be introduced to one's wort. Cell division follows an exponential growth pattern; therefore, the increase in cell count for yeast can be calculated as:
initial_yeast_cell_count * 2^(elapsed_time_in_minutes_since_the_start_of_the_ growth_phase / 90), where the symbol ""^" denotes raised to the power of.
Examples
Yeast cell count after 90 minutes of growth
initial_yeast_cell_count * 2^(90 / 90) = 2 x initial_yeast_cell_count
Yeast cell count after 6 hours of growth
initial_yeast_cell_count * 2^(360 / 90) = 16 x initial_yeast_cell_count
There is a period between pitching and the growth phase (a.k.a. exponential or log phase) known as the lag phase. The lag phase is where the yeast cells that were pitched prepare themselves for growth.
With the above said, it is easy to now see why a Wyeast smack pack is far too little yeast to ensure a clean fermentation. Bacteria divide three times faster than yeast; therefore, a tiny amount bit of bacteria can completely overwhelm a yeast culture.
Examples
Yeast cell count after 6 hours of growth
initial_yeast_cell_count * 2^(360 / 90) = 16 x initial_yeast_cell_count
Bacteria cell count after 6 hours of growth
initial_bacteria_cell_count * 2^(360 / 30) = 4,096 x initial_bacteria_cell_count
Yeast cell count after 12 hours of growth
initial_yeast_cell_count * 2^(720 / 90) = 256 x initial_yeast_cell_count
Bacteria cell count after 12 hours of growth
initial_bacteria_cell_count * 2^(720 / 30) = 16,777,216 x initial_bacteria_cell_count
Yeast cell count after 24 hours of growth
initial_yeast_cell_count * 2^(1440 / 90) = 65,536 x initial_yeast_cell_count
Bacteria cell count after 24 hours of growth
initial_bacteria_cell_count * 2^(1440 / 30) = 281,474,976,710,656 x initial_bacteria_cell_count
In closing, the off flavors that result from underpitching have almost nothing to do with one's pitching yeast and everything to do with one's house microflora.